4.MD Tasks - 3

Formative Instructional and Assessment Tasks

Domain

Cluster

Standard(s)

Materials

Measuring the Jump Ropes

4.MD.1-Task 1

Measurement and Data

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.1

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in.

Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches

listing the number pairs (1, 12), (2, 24), (3, 36), ...

Paper and pencil

Measuring the Jump Ropes

There are some jump ropes in a container in the gym. The students need to sort them by length.

Sally picks all the ropes that are 40 inches or shorter

Mary picks all the ropes between 41 and 50 inches long.

Tanya picks all the ropes that are between 51 and 62 inches long.

Jose picks all the ropes that are between 63 and 74 inches long.

Lebron picks all the ropes that are 75 inches or longer.

Part 1:

Based on the data below, how many jump ropes does each person pick up?

3 ft 2 ft 5 ft 4 ft 4 ft 3 ft 5 ft

7 ft

Part 2:

6 ft 6 ft 6 ft 3 ft 5 ft 4 ft

Another bin is found. After students add the ropes below to their pile, how many do they each have?

6 ft 2 in 4 ft 3 in 2 ft 11 in 3 ft 4 in 3 ft 5 in 3 ft 11 in 6 ft 8 in


Part 3:

Describe how you solved the tasks in Part Two.

Level I

Limited Performance



Students make more than 2 errors.

Rubric

Level II

Not Yet Proficient



Students make 1 or 2 errors OR their explanation in Part 3 is not accurate.

Level III

Proficient in Performance



The student provides correct answers. Part 1:

Sally: 4 ropes, Mary: 3 ropes, Tanya: 3 ropes,

Jose: 2 ropes, Lebron: 1 rope.



Part 2: Sally: 4 ropes. Mary: 4 ropes, Tanya: 2 ropes, Jose: 3 ropes, Lebron: 1 rope.



Part 3: Student discusses multiplying the number of feet by 12 and adding the number of inches.

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE


Standards for Mathematical Practice

1. Makes sense and perseveres in solving problems.

2. Reasons abstractly and quantitatively.

3. Constructs viable arguments and critiques the reasoning of others.

4. Models with mathematics.

5. Uses appropriate tools strategically.

6 . Attends to precision.

7. Looks for and makes use of structure.

8. Looks for and expresses regularity in repeated reasoning.



Measuring the Jump Rope

There are some jump ropes in a container in the gym. The students need to sort them by length.

Sally picks all the ropes that are shorter than 40 inches.

Mary picks all the ropes between 41 and 50 inches long.

Tanya picks all the ropes that are between 51 and 62 inches long.

Jose picks all the ropes that are between 63 and 74 inches long.

Lebron picks all the ropes that are longer than 75 inches.

Part 1: Based on the data below, how many jump ropes does each person pick up?

3 ft

7 ft

2 ft

6 ft

Part 2: Another bin is found. After students add the ropes below to their pile, how many do they each have?

5 ft

6 ft

4 ft

6 ft

4 ft

3 ft

3 ft

5 ft

5 ft

4 ft



Part 3: Describe how you solved the tasks in Part Two.



Domain

Cluster

Standard(s)

How Long Did I Jump?

4.MD.1-Task 2



4.MD.1

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.

Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Materials Paper and pencil


At school three students are have a jumping competition to see who can jump the farthest.

Miguel, Nancy, and Sarah both jump between 3 and 4 feet.

Part 1:

A.

If Nancy jumps farther than Miguel but shorter than Sarah, what are possible distances that each person jumped in inches?

B.

If all 3 people jumped farther than 3 feet 6 inches, what are the possible distances that each person could have jumped in inches?

C.

If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how long did each person jump?

Part 2:

Write a sentence describing how you found the distances that each person jumped in inches.

Rubric

Level I Level II Level III

Limited Performance






Not Yet Proficient

Students make

1 or 2 errors




The student provides correct answers. Part 1: A- Distances must be between 37 and 47 inches. Miguel must have the smallest distance, Nancy must have the 2 nd

longest, and OR their explanation in

Part 3 is not accurate.

Sarah must have the longest distance. B- Same as A, but the distances must be between 43 and 47 inches. C- Miguel- 44 inches, Nancy- 45 inches, Sarah- 46 inches.



AND there is a clear and accurate explanation about how they found the distances in inches.













At school three students are have a jumping competition to see who can jump the farthest?

Miguel, Nancy, and Sarah both jump between 3 and 4 feet.

Part 1:

A.

If Nancy jumps farther than Miguel but shorter than Sarah, what are possible distances that each person jumped in inches?

B.

If all 3 people jumped farther than 3 feet 6 inches, what are the possible distances that each person could have jumped in inches?

C.

If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how long did each person jump?

Part 2: Write a sentence describing how you found the distances that each person jumped in inches.



Domain

Cluster

Standard(s)

Materials

Baby Weights

4.MD.1-Task 3



4.MD.1




Paper and pencil, activity sheet (attached)

Baby Weights

Using the table below, answer the following questions:

Baby Gender

Samuel Boy

Nicole Girl

TJ Boy

Weight

7 and 2/4 pounds

7 and 7/8 pounds

1 and 3/4 pounds heavier than Samuel

Tyrette Girl 1 and 4/8 of a pound heavier than Nicole

Part 1:

What is the weight of each baby in pounds?

What is the weight of each baby in ounces?

Part 2:

How many pounds do the boys weigh? How many ounces do the boys weigh?

How many pounds do the girls weigh? How many ounces do the girls weigh?

Part 3:

What was the total weight of all of the babies in pounds?

What was the total weight of all of the babies in ounces?

Part 4:

Write a sentence about a strategy that you used to convert the babies’ weights from pounds to ounces.

Level I

Limited

Performance




Level II

Not Yet Proficient



Students make 1 or 2 errors OR their explanation is not accurate.

Rubric

Level III




Part 1: Samuel- 7 and 2/4 pounds, 120 ounces;

Nicole- 7 and 7/8 pounds, 126 ounces; TJ- 9 and

1/4 pounds, 148 ounces; Tyrette- 9 and 3/8 pounds, 150 ounces



Part 2: Boys- 16 and 3/4 pounds, 268 ounces;

Girls- 17 and 2/8 or 17 and 1/4 pounds; 276 ounces.



Part 3: Ounces: 34 pounds; 544 ounces



Part 4: The sentence includes a logical and accurate approach of converting units.














Baby Weights

Using the table below, answer the following questions:

Baby Gender Weight

Samuel Boy 7 and 2/4 pounds

Nicole Girl

TJ Boy

7 and 7/8 pounds

1 and 3/4 pounds heavier than Samuel

Tyrette Girl 1 and 4/8 of a pound heavier than Nicole

Part 1:

What is the weight of each baby in pounds?

What is the weight of each baby in ounces?

Part 2:

How many pounds do the boys weigh? How many ounces do the boys weigh?

How many pounds do the girls weigh? How many ounces do the girls weigh?

Part 3:

What was the total weight of all of the babies in pounds?

What was the total weight of all of the babies in ounces?

Part 4:

Write a sentence about a strategy that you used to convert the babies’ weights from pounds to ounces.


Domain

Cluster

Standard(s)

Materials


Shipping Packages

4.MD.1-Task 4



4.MD.1






Four friends are each sending packages . Use the table below to answer the following questions:

Package

Sarah’s box

Karen’s box

Tim’s box

Steve’s box

Weight

25 and 6/8 pounds

24 and 5/8 pounds

29 and 7/8 pounds

24 and 2/8 pounds

Part 1:

What is the weight of each person’s box in ounces?

Part 2:

What is the combined weight of each person’s box in pounds?

What is the combined weight of each person’s box in ounces?

Part 3:

Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if they are between 400 and 500 ounces. How much does each package cost?

Part 4:

If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh the same amount, how much do all of those boxes weigh in pounds? Write a sentence explaining how you found your answer.



Rubric

Limited Performance



Level I




Level II

Not Yet Proficient

Students make 1 or 2 errors

OR their explanation is not accurate.

Level III




Part 1: Sarah: 412 ounces; Karen: 394 ounces; Tim: 478 ounces; Steve: 388 ounces.



Part 2: 104 and 4/8 pounds; 1,672 ounces



Part 3: Karen and Steve will have to pay $10.

Sarah and Tim will have to pay $15.

 Part 4: Sarah’s 3 boxes would weigh 77 and

1/4 pounds. Tim’s 4 boxes would weigh 119 and 2/4 pounds. The combined weight would be 196 and 3/4 pounds.













Four friends are each sending packages . Use the table below to answer the following questions:

Package

Sarah’s box

Weight

25 and 6/8 pounds

Precious’ box

24 and 5/8 pounds

Tim’s box

29 and 7/8 pounds

Steve’s box

24 and 2/8 pounds

Part 1:

What is the weight of each person’s box in ounces?

Part 2:

What is the combined weight of each person’s box in pounds?

What is the combined weight of each person’s box in ounces?

Part 3:

Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if they are between 400 and 500 ounces. How much does each package cost?

Part 4:

If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh the same amount, how much do all of those boxes weigh in pounds? How much do all of the boxes weigh in ounces? Write a sentence explaining how you found your answer.



Domain

Cluster

Standard(s)

Materials

Relay Running

4.MD.1-Task 5



4.MD.1





Relay Running

The following runners are on the same relay team for the 4,000 meter race. Here are their times:

Runner Time

Alberto 2 minutes and 55 seconds

Kate

Kelly

3 minutes and 8 seconds


Matt 2 minutes and 58 seconds

Part 1:

What was the time of each runner in terms of only seconds?

Part 2:

Write a sentence explaining how you solved the questions in Part 1.

Rubric

Level I

Limited Performance




Level II

Not Yet Proficient





Level III




Part 1: Albert-175 seconds, Kate-188 seconds, Kelly-197 seconds, Matt-178 seconds



Part 2: The sentence shows an appropriate way of solving the problems in Part 1.












Relay Running

The following runners are on the same relay team for the 4,000 meter race. Here are their times:

Runner Time

Alberto 2 minutes and 55 seconds

Kate

Kelly



Matt 2 minutes and 58 seconds

Part 1:

What was the time of each runner in terms of only seconds?

Part 2:




Domain

Cluster

Standard(s)

Materials

Off to the Races

4.MD.1-Task 6



4.MD.1






The following runners just completed the Seaside Marathon race where they ran 26.2 miles.

Runner Time

Angela 3 hours, 25 minutes, 15 seconds

Paul

Sandy

3 hours, 26 minutes, 30 seconds


Jason 3 hours, 39 minutes, 15 seconds

Part 1:

What was the time of each runner in terms of only minutes and seconds (e.g., 185 minutes and 15 seconds)?

Part 2:


Rubric

Limited Performance



Level I


Level II

Not Yet Proficient





Level III




Part 1: Angela: 205 min, 15 sec; Paul: 206 min, 30 sec; Sandy: 221 min, 45 sec; Jason:

219 min, 15 sec



Part 2: The sentence shows an appropriate way of solving the problems in Part 1.













The following runners just completed the Seaside Marathon race where they ran

26.2 miles.

Runner Time

Angela 3 hours, 25 minutes, 15 seconds

Paul

Sandy



Jason 3 hours, 39 minutes, 15 seconds

Part 1:

What was the time of each runner in terms of only minutes and seconds (e.g., 185 minutes and 15 seconds)?

Part 2:




Domain

Cluster

Standard(s)

Mapping My Run

4.MD.1-Task 7



4.MD.1




Paper and pencil, activity sheet (attached) Materials

Mapping A Run

On her iPhone Molly was able to track how far she ran each day this week. Here are her distances.

Day

Monday

Distance

5 km, 430 m, 0 cm

Tuesday

Wednesday

4 km, 789 m, 98 cm

6 km, 967 m, 56 cm

Thursday 5 km, 5 m, 5 cm

Part 1:

How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters and 38 centimeters)?

Part 2:

Write a sentence explaining how you found out the distance that she ran.

Rubric

Level I

Limited Performance






Level II

Not Yet Proficient



Level III




Part 1: Monday: 5,430 m and 0 cm; Tuesday:

4,789 m and 98 cm; Wednesday: 6,967 m and 56 cm; Thursday: 5,005 m and 5 cm.



Part 2: The sentence is logical and accurate.












Mapping A Run

On her iPhone Molly was able to track how far she ran each day this week. Here are her distances.

Day

Monday

Distance

5 km, 430 m, 0 cm

Tuesday 4 km, 789 m, 98 cm

Wednesday 6 km, 967 m, 56 cm

Thursday 5 km, 5 m, 5 cm

Part 1:

How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters and 38 centimeters)?

Part 2:

Write a sentence explaining how you found out the distance that she ran.



Domain

Cluster

Standard(s)

Filling the Jugs

4.MD.1-Task 8



4.MD.1





Filling the Jug

For a class project there was a large 10 Liter jug that had to be filled with water.

Unfortunately, the class only had a container marked in milliliters.

Part 1:

Complete the table below.

Amount in the jug Amount in Milliliters

1 Liter

1 Liter and 250 mL

1 Liter and 750 mL

2 Liters

2 Liters and 400 mL

2 Liters and 756 mL

3 Liters

Part 2:

Write a sentence to explain how you found the answer to one of the rows of the table.

Rubric

Limited Performance



Level I


Level II

Not Yet Proficient





Level III




Part 1: 1 L = 1,000 mL; 1 L, 250 mL; 1,250 mL; 1L, 750 mL= 1,750 mL; 2 L = 2,000 mL; 2L, 400 mL = 2,400 mL; 2L, 756 mL;

2,756 mL; 3L = 3,000 mL



Part 2: The sentence is logical and accurate.












Filling the Jug

For a class project there was a large 10 Liter jug that had to be filled with water.

Unfortunately, the class only had a container marked in milliliters.

Part 1:


Amount in the jug Amount in Milliliters

1 Liter

1 Liter and 250 mL

1 Liter and 750 mL

2 Liters

2 Liters and 400 mL

2 Liters and 756 mL

3 Liters

Part 2:




Domain

Cluster

Standard(s)

Making Punch

4.MD.1-Task 9



4.MD.1





Making Punch

For a party Mrs. Laney is making punch. She filled a few different large punch bowls.

Part 1:


Punch Bowl

2 Liters and 5 milliliters





Amount in Milliliters


Part 2:


Rubric

Limited Performance



Level I


Level II

Not Yet Proficient





Level III




Part 1: 2 L, 5 mL = 2,005 mL; 2L, 50 mL =

2,050 mL; 2L, 500 mL = 2,500 mL; 3 L, 8 mL = 3,008 mL; 3L, 80 mL = 3,080 mL; 3

L, 800 mL = 3,800 mL



Part 2: The explanation contains an accurate explanation.












Making Punch

For a party Mrs. Laney is making punch. She filled a few different large punch bowls.

Part 1:


Punch Bowl Amount in Milliliters







Part 2:




Domain

Cluster

Standard(s)

Weighing the Books

4.MD.2-Task 1



4.MD.2

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Paper and pencil Materials


Mrs. Floyd and her classmates want to know how heavy a few of the books in their classroom are.

Part 1:

They want to know the masses of the objects in ounces; however the scale only gives the mass in pounds. Using the table below, find out how many ounces each book is.

Math book 2 1/2 pounds

Science book 3 1/3 pounds

Dictionary 5 1/8 pounds

Part 2:

Two copies of one book and two copies of another book weigh a total of 6 pounds. Each book weighs a whole number of ounces. How many ounces could each book weigh?

Explain how you solved this problem.

Rubric


Limited Performance






Not Yet Proficient






Part 1: Math: 40 ounces, Science: 53 1/3 ounces, Dictionary: 82 ounces.



Part 2: The books should have a combined weight of 48 ounces, since 2 copies of both books will be 6 pounds or 96 ounces.



AND there is a clear and accurate explanation about how they found the distances in inches.













Mrs. Floyd and her classmates want to know how heavy a few of the books in their classroom are.

Part 1:

They want to know the masses of the objects in ounces, however the scale only gives the mass in pounds. Using the table below, find out how many ounces each book is.

Math book 2 1/2 pounds _______oz

Science book 3 1/3 pounds _______oz

Dictionary 5 1/8 pounds _______oz

Part 2:

Two copies of one book and two copies of another book weigh a total of 6 pounds. Each book weighs a whole number of ounces. How many ounces could each book weigh? Explain how you solved this problem.



Domain

Cluster

Standard(s)

Materials

Getting Ready for School

4.MD.2-Task 2



4.MD.2


Paper and pencil


The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:

Eat breakfast: 15 minutes

Shower: 8 minutes

Get dressed: 7 minutes

Read a book: 12 minutes

Part 1:

What is the latest that Steve can get up and still be on time for the bus?

Part 2:

It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to eat breakfast. What is the latest Rachel can get up and still be on time for the bus? Write a sentence to explain how you found your answer.

Rubric

Level I

Limited Performance




Level II

Not Yet Proficient




OR their explanation in

Part 3 is not accurate.



Level III




Part 1: Steve needs to be up by 7:33 a.m.

Part 2: Rachel needs to be up by 7:21 a.m.



AND the explanation is clear and accurate.











The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:

Eat breakfast: 15 minutes

Shower: 8 minutes

Get dressed: 7 minutes

Read a book: 12 minutes

Part 1:

What is the latest that Steve can get up and still be on time for the bus?

Part 2:

It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to eat breakfast. What is the latest Rachel can get up and still be on time for the bus?

Write a sentence to explain how you found your answer.



Domain

Cluster

Standard(s)

Materials

Adding Up and Comparing Our Jumps

4.MD.2-Task 3



4.MD.2


Paper and pencil



Part 1:

Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy.

Sarah jumped 9 inches longer than Miguel.

How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?

How long did each person jump in only inches?

Part 2:


Part 3:

What was the combined length that all three students jumped in inches? What was their distance in feet and inches?

Part 4:

Three other students jumped a combined distance of 15 feet. How much further did they jump compared to the combined distance of Nancy, Miguel, and Sarah?

Level I

Limited Performance




Rubric

Level II

Not Yet Proficient





Level III




Part 1: Nancy: 3 ft, 11 in or 47 in; Miguel: 4 ft, 4 in or 52 in; Sarah: 5 ft, 1 in or 61 in.



Part 2: The sentence contains a logical and accurate description.



Part 3: 160 inches or 13 ft 4 in.



Part 4: The other students jumped 1 ft and 8 inches further.
















Part 1:

Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy.

Sarah jumped 9 inches longer than Miguel.



Part 2:


Part 3:

What was the combined length that all three students jumped in inches?

What was their distance in feet and inches?

Part 4:

Three other students jumped a combined distance of 15 feet. How much further did they jump compared to the combined distance of Nancy, Miguel, and Sarah?


Domain

Cluster

Standard(s)

Materials


Adding Up and Comparing Our Jumps II

4.MD.2-Task 4



4.MD.2


Paper and pencil



Part 1:

Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy.

Mitch jumped 11 inches longer than Yani.



Part 2:


Part 3:


Part 4:

Three other students jumped a combined distance of 14 feet. How much further did they jump compared to the combined distance of Timothy, Yani, and Mitch?



Rubric


Limited Performance






Not Yet Proficient





Part 1: Timothy- 3 feet 10 inches or 46 inches;

Yani- 4 ft and 2 inches or 50 inches; Mitch- 5 ft 1 inch or 61 inches



Part 2: The sentence accurately describes an appropriate process to find out each distance in inches.



Part 3: The combined distance was 157 inches or

13 feet 1 inch.



Part 4: The three other students jumped 11 inches farther than Timothy, Yani, and Mitch.














Part 1:

Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy.

Mitch jumped 11 inches longer than Yani.



Part 2:


Part 3:


Part 4:

Three other students jumped a combined distance of 14 feet. How much further did they jump compared to the combined distance of Timothy, Yani, and Mitch?



Domain

Cluster

Standard(s)

Materials

Task

Area & Perimeter Exploration

4.MD.3-Task 1



4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Paper and pencil, graph paper or square tiles

Examining the relationship between area and perimeter and using area and perimeter formulas for quick calculation.

Activity 1 :

Create all the possible arrays with an area of 36 square units.

Draw them on grid paper and label their dimensions.

How can you be sure that you found all the possible arrays with an area of 36 square units?

Find the perimeter for each figure.

What do you notice about the shapes and their perimeters?

What is the relationship between the perimeter and the shape of an array?

Activity 2:

Create all the possible arrays with a perimeter of 36 units.

Draw your arrays on grid paper and label their dimensions.

Use a chart to keep track of the area and dimensions for each rectangle.

How can you be sure that you found all the possible arrays with a perimeter of 36 units?

What do you notice about the shapes and their perimeters?

What is the relationship between the area and the shape of an array?

Activity 3:

What generalizations can be made about the relationship between the area and perimeter of a figure?

How could this this information be used to solve a problem in real life? When might it be useful to have this information?

Possible Solution:

Activity 1: All have area of 36 square units.

Perimeter dimensions

74 units 1 x 36

40 units 2 x 18

30 units 3 x 12

26 units 4 x 9

24 units 6 x 6

Possible conclusions: The closer a shape gets to being a square, the smaller its perimeter.



Activity 2: All have a perimeter of 36 units.

Area dimensions

17 1 x 17

32 2 x 16

45 3 x 15

56 4 x 14

65 5 x 13

72 6 x 12

77 7 x 11

80 8 x 10

81 9 x 9

Possible response: The closer a shape gets to being a square, the larger its area.

Squares have the largest possible area and the smallest possible perimeter.

Level I

Limited Performance

 The student is unable to find all the possible figures with an area of 36 and/or calculate the perimeter for each figure. The student is unable to find all the possible arrays with a perimeter of 36 and/or their areas. The student does not have an efficient strategy to check to make sure that s/he has found all the possible arrays that fit the requirements.

They are unable apply the formula for area or perimeter to perform the required calculations. problem.

Rubric

Level II

Not Yet Proficient

 The student is able to find all the possible arrays, areas, and perimeters for Activity 1 and

Activity 2. They are unable to make generalizations about the relationship between area and perimeters of squares and rectangles. They are unable to generate an example of how this relationship might be useful in solving a real world




3. Constructs viable arguments and critiques the reasoning of others.



6 . Attends to precision.

7. Looks for and makes use of structure.


Level III


 The student is able to find all the possible arrays, areas, and perimeters for Activity 1 and

Activity 2. They are able to make generalizations about the relationship between area and perimeters of squares and rectangles, and to generate at least one example of how this relationship might be useful in solving a real world problem.



Area & Perimeter Exploration

Activity 1 :

 Create all the possible arrays with an area of 36 square units.

 Draw them on grid paper and label their dimensions.

 How can you be sure that you found all the possible arrays with an area of 36 square units?

 Find the perimeter for each figure.

 What do you notice about the shapes and their perimeters?

 What is the relationship between the perimeter and the shape of an array?

Activity 2:

 Create all the possible arrays with a perimeter of 36 units.

 Draw your arrays on grid paper and label their dimensions.

 Use a chart to keep track of the area and dimensions for each rectangle.

 How can you be sure that you found all the possible arrays with a perimeter of

36 units? What do you notice about the shapes and their perimeters?

 What is the relationship between the area and the shape of an array?

Activity 3:

 What generalizations can be made about the relationship between the area and perimeter of a figure?

 How could this this information be used to solve a problem in real life? When might it be useful to have this information?



Domain

Cluster

Standard(s)

Materials

Putting Down Carpet

4.MD.3 - Task 2



4.MD.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation

with an unknown factor.

Plastic square tiles, Paper, Pencil, Graph paper (optional)


Part 1:

You want to carpet 3 rooms of a house. Using the dimensions below, determine how much carpet is needed.

Room 1: Perimeter is 38 yards and the width of the room is 12 yards.

Room 2: Perimeter is 50 yards and the width is 13 yards.


For each room, determine how much carpet is needed.

Part 2:

Write a sentence and explain how you solved this task.

Rubric

Level I

Limited Performance




Level II

Not Yet Proficient





Level III




Part 1: Room 1: Width is 12, Length is 7.

Area is 84 square yards. Room 2: Width is

13 yards, Length is 12 yards. Area is 156 square yards. Room 3: Width is 10, Length is

13. Area is 130 square yards.



Part 2: The explanation is clear and accurate.













Part 1:

You want to carpet 3 rooms of a house. Using the dimensions below, determine how much carpet is needed.

Room 1: Perimeter is 38 yards and the width of the room is 12 yards.



For each room, determine how much carpet is needed.

Part 2:




Domain

Cluster

Standard(s)

Fencing Yards

4.MD.3 - Task 3



4.MD.3



Plastic square tiles, Paper, Pencil, Graph paper (optional) Materials

Fencing Yards

Part 1:

For a summer job, your older brother is working for a fencing company. Determine how much fencing is needed for each of these rectangular yards.

Yard 1: Area is 500 square meters. Length is 25 meters.



Part 2:




Level II

Not Yet Proficient



Rubric

Level I

Limited Performance




Level III




Part 1: Yard 1: Width is 20 meters. Fencing:

90 meters. Yard 2: Width is 63 meters.

Fencing: 144 meters. Yard 3: Width is 184 meters. Fencing is 376 meters.



Part 2: The explanation is clear and accurate.












Fencing Yards

Part 1:

For a summer job, your older brother is working for a fencing company. Determine how much fencing is needed for each of these rectangular yards.




Part 2:





Making a Dog Pen

4.MD.3 - Task 4

Domain

Cluster

Standard(s)

Materials


4.MD.3



Plastic square tiles, Paper, Pencil, Graph paper (optional)


Part 1:

You want to make a rectangular dog pen using 20 yards of fencing. The side lengths must be in whole yards. Create as many different rectangular pens as you can.

Part 2:

Which dog pen gives your dog the most space to run around and play in? Write a sentence explaining how you know.

Part 3:

You want to build the rectangular dog pen with 20 yards of fencing against your house which is 20 yards wide. Which dimensions will give you the most space for your dog?

Level I

Limited Performance




Level II

Not Yet Proficient




Rubric

Level III




Part 1: The dimensions must add up to 10. 9x1,

8x2, 7x3, 6x4, 5x5.



Part 2: The 5x5 pen gives the most space, 25 square yards. AND the explanation is clear and accurate.



Part 3: The 10x5 rectangle gives the most space. The 10 yard side runs parallel to the house while the 5 yard sides connect the house to the other side.













Part 1:

You want to make a rectangular dog pen using 20 yards of fencing. The side lengths must be in whole yards. Create as many different rectangular pens as you can.

Part 2:

Which dog pen gives your dog the most space to run around and play in? Write a sentence explaining how you know.

Part 3:

You want to build the rectangular dog pen with 20 yards of fencing against your house which is 20 yards wide. Which dimensions will give you the most space for your dog?



Domain

Cluster

Standard(s)

Materials

Task

Reading Survey

4.MD.4 - Task 1


Represent and interpret data.

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Paper, pencils, white boards and dry-erase markers (optional)

Directions for students:

 As a class, have students survey 10 classmates and ask them “How long do you think fourth graders should read each night at home?” They can choose ¼, ½, ¾ or 1 hour.

Students should record results on a piece of paper.



Create a line plot to represent the data.



Have students write a sentence about an observation that they notice from the line plot.



If you were using this line plot to make a decision about how long students should read each night, which time would you choose? Why?

Limited Performance



Incorrect answer and work are given.

Level I

Rubric

Level II

Not Yet Proficient



Finds the correct answer, but there may be inaccuracies or incomplete justification of solution OR



Uses partially correct work but does not have a correct solution.


1 . Makes sense and perseveres in solving problems.



4. Models with mathematics.

5. Uses appropriate tools strategically.

6. Attends to precision.



Level III




Accurately surveys and makes a line plot, and analyses the results.



Uses an appropriate model to represent and justify the solution.



How High Did it Bounce?

4.MD.4-Task 2

Measurement and Data Domain

Cluster

Standard(s)

Materials


4.MD.4

Make a line plot to display a data set of measurements in fractions of a unit (1/2,

1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the

difference in length between the longest and shortest specimens in an insect collection.

Paper, pencil, Activity sheet


A class measures how high a bouncy ball will bounce compared to the height of the wall.

Based on the data, make a line plot to display the data.

3/8 5/8 7/8 6/8 5/8 6/8

6/8

5/8

5/8

7/8

4/8

5/8

4/8

6/8

2/8

4/8

6/8

5/8

A) How many bouncy balls went halfway up the wall or higher?

B) How may bouncy balls went 3/4 of the wall or higher?

C) What is the combined height of all of the heights of the bouncy balls?

Level I

Limited Performance






Level II

Not Yet Proficient

Rubric


Level III




A) 16 balls, B) 7 balls, C) 11 and 3/8 of the wall or 91 feet high.













A class measures how high a bouncy ball will bounce compared to the height of the wall. Based on the data, make a line plot to display the data.

3/8

6/8

5/8

5/8

7/8

4/8

6/8

4/8

5/8

2/8

6/8

6/8

5/8 7/8 5/8 6/8 4/8 5/8

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 1

A) How many bouncy balls went halfway up the wall or higher?

B) How may bouncy balls went 3/4 of the wall or higher?

C) If the wall is 8 feet high, what is the combined height of all of the heights of the bouncy balls?




Measuring Strings

4.MD.4-Task 3

Domain

Cluster

Standard(s)

Materials


4.MD.4

Make a line plot to display a data set of measurements in fractions of a unit (1/2,

1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the

difference in length between the longest and shortest specimens in an insect collection.

Paper, pencil, Activity sheet


A basket of strings is measured by the class and graphed. Based on the line plot:

1)

How many strings are ½ of a foot or longer?

2) How many strings are shorter than 3/8 of a foot?

3) If students put the string together that is 1/8 or 2/8 of a foot long, how long would that string be?

4) If students put all of the pieces of string together, how long would that string be?

Level I

Limited Performance






Level II

Not Yet Proficient

Rubric


Level III




1) 7. 2) 6, 3) 9/8 or 1 and 1/8, 4) 8 and 6/8 or 8 and 3/4













A basket of strings is measured by the class and graphed. x x

Lengths of string (feet) x x x x x x x x x

x

x

x

x

x

X

X

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 1

Based on the line plot:

1) How many strings are more than ½ of a foot or longer?

2) How many strings are shorter than 3/8 of a foot?

3) If students put the string together that is 1/8 or 2/8 of a foot long, how long would that string be?

4) If students put all of the pieces of string together, how long would that string be?



Domain

Cluster

Standard(s)

Materials

Task

Intersecting Roads

4.MD.5 – Task 1


Geometric measurement: understand concepts of angle and measure angles.

4.MD.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.6

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Task handout, Protractor (optional)


Circle-town is shaped like a circle. All of the roads start in the center of the town and extend from the center like rays.

Part 1:

On the map draw the following roads and label the measure of each angle. a) Smith Street extends completely horizontal to the right of the center of town. b)

Smith Street and Main Street form a 45 degree angle. c)

Thompson Street forms a 30 degree angle with Main Street. d) Young Avenue forms a 90 degree angle with Thompson Street. e)

Turnberry forms a 120 degree angle with Young Avenue.

Part 2:

Write an explanation about how you know your answers are correct in Part 1.

Level I

Limited Performance

 The student is unable to use strategies to find correct answers to any aspect of the task. a)

Level II

Not Yet Proficient

 The student has between 1 and 2 errors.

Rubric

Level III


 The answers are correct.

 Part 1: Roads are drawn correctly and angles are correctly labeled.

 Part 2: The explanation is clear and accurate.









8. Looks for and expresses regularity in repeated reasoning




Circle-town is shaped like a circle. All of the roads start in the center of the town and extend from the center like rays.

Part 1:

On the map draw the following roads and label the measure of each angle. a)

Smith Street extends completely horizontal to the right of the center of town. b)

Smith Street and Main Street form a 45 degree angle. c)

Thompson Street forms a 30 degree angle with Main Street. d)

Young Avenue forms a 90 degree angle with Thompson Street. e)

Turnberry forms a 120 degree angle with Young Avenue.

Part 2:

Write an explanation about how you know your answers are correct in Part 1.

Extension: Create your own town and give direction as noted above.



Domain

Cluster

Standard(s)

Materials

Task

Going Different Directions

4.MD.6 – Task 1



4.MD.6


4.MD.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Task handout, Protractor (optional)


Pairs of students worked together to explore the idea of creating an angle.

Part 1 : Each student represents a point and each walk represents a ray. Draw the angle each situation below creates. a)

Students stood back to back and walked away from each other; b) One student faced forward while the other student turned 30 degrees and both students walked forward; c)

One student faced forward while the other student turned 90 degrees and both students walked forward; d)

One student faced forward while the other student turned 120 degrees and both students walked forward.

Part 2: Explain how you solved the tasks above.

Level I

Limited Performance

 The student is unable to use strategies to find correct answers to any aspect of the task. b)

Level II

Not Yet Proficient


Rubric

Level III



 Part 1: Angles are drawn correctly. A is a 180 degree or straight angle.














Pairs of students worked together to explore the idea of creating an angle. Each student represents a point and each walk represents a ray. Draw the angle each situation below creates.

Part 1:

Draw each angle when: c)

Students stood back to back and walked away from each other. d) One student faced forward while the other student turned 30 degrees and both students walked forward. e)

One student faced forward while the other student turned 90 degrees and both students walked forward. f)

One student faced forward while the other student turned 120 degrees and both students walked forward.

Part 2:

Explain how you solved the tasks above.



Domain

Cluster

Standard(s)

Materials

Task

Making Shapes

4.MD.6 – Task 2



4.MD.6


4.MD.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a . An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b.

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Task handout, Geoboard, Protractor

Making Shapes

Part 1:

On the geoboard make the following shapes. Below, draw the shape and write the measurement of each angle. a)

A rectangle b) A trapezoid c)

A parallelogram that is not a rectangle d)

A right triangle e) An isosceles triangle f)

An obtuse triangle

Part 2: Write an explanation describing how you measured each of the angles in the isosceles triangle.

Level I

Limited Performance

 The student is unable to use strategies to find correct answers to any aspect of the task. g) Level II

Not Yet Proficient


Rubric

Level III



 Part 1: The shapes are drawn correctly and angle measures are correctly labeled.













Making Shapes

Part 1:

On the geoboard make the following shapes. Below, draw the shape and write the measurement of each angle. a)

A rectangle b)

A trapezoid c)

A parallelogram that is not a rectangle d)

A right triangle e)

An isosceles triangle f)

An obtuse triangle

Part 2:

Write an explanation describing how you measured each of the angles in the isosceles triangle.




Adding Up Angles

4.MD.7-Task 1

Domain

Cluster

Standard(s)

Materials


4.MD.7

Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Paper, pencil, Protractor


A 90 degree angle is divided into two smaller angles.

Part 1:

What type of angles are both of the smaller angles? How do you know?

Part 2:

Give 3 possible combinations for the measurements of both angles. For each, draw the angles and write the angle measure.

Level I

Limited Performance






Level II

Not Yet Proficient

Rubric


OR the drawings are not close to the angle measure.

Level III




Part 1: Both angles have to be acute angles since the sum of both is 90 degrees.



Part 2: The sum of both angles has to be 90 degrees for all 3 answers AND the drawings are close to the angle measure.













A 90 degree angle is divided into two smaller angles.

Part 1:

What type of angles are both of the smaller angles? How do you know?

Part 2:

Give 3 possible combinations for the measurements of both angles. For each, draw the angles and write the angle measure.



Domain

Cluster

Standard(s)

Materials

How Can We Split Angles?

4.MD.7-Task 2



4.MD.7

Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Paper, pencil, Protractor


Part 1:

Use a protractor to split a 135 degree angle the following ways:

A) A right angle, a 35 degree angle and another acute angle. What is the measure of the other angle?

B) A right angle and another angle. What is the measure of the other angle?

C) A 120 degree angle and another angle. What is the measure of the other angle?

D) 3 angles that are the same size.

E) A 15 degree angle and 2 angles that are the same size. What is the measure of the other angles?

Part 2:

Describe how you solved one of the tasks above.

Rubric

Level I

Limited Performance




Level II

Not Yet Proficient




Level III




Part 1: A) The other angle is 10 degrees. B)

The other angle is 45 degrees. C) The other angle is 15 degrees. D) Each angle is 45 degrees. E) The other angles are each 60 degrees.



Part 2: Description is clear and accurate.













Part 1:

Use a protractor to split a 135 degree angle the following ways:

A) A right angle, a 35 degree angle and another acute angle. What is the measure of the other angle?

B) A right angle and another angle. What is the measure of the other angle?

C) A 120 degree angle and another angle. What is the measure of the other angle?

D) 3 angles that are the same size. What is the measure of each of the angles?

E) A 15 degree angle and 2 angles that are the same size. What is the measure of the other angles?

Part 2:

Describe how you solved one of the tasks above.


4.MD Tasks - 3

Measuring the Jump Rope

How Long Did I Jump?

Baby Weights

Shipping Packages

Relay Running

Off to the Races

Mapping A Run

Filling the Jug

Making Punch

Weighing the Books

Getting Ready for School

Adding Up and Comparing Our Jumps

Adding Up and Comparing Our Jumps II

Area & Perimeter Exploration

Putting Down Carpet

Fencing Yards

Making a Dog Pen

How High Did it Bounce?

Measuring Strings

Intersecting Roads

Going Different Directions

Making Shapes

Adding Up Angles

How Can We Split Angles?

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4.MD Tasks - 3

Measuring the Jump Rope

How Long Did I Jump?

Baby Weights

Shipping Packages

Relay Running

Off to the Races

Mapping A Run

Filling the Jug

Making Punch

Weighing the Books

Getting Ready for School

Adding Up and Comparing Our Jumps

Adding Up and Comparing Our Jumps II

Area & Perimeter Exploration

Putting Down Carpet

Fencing Yards

Making a Dog Pen

How High Did it Bounce?

Measuring Strings

Intersecting Roads

Going Different Directions

Making Shapes

Adding Up Angles

How Can We Split Angles?

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